Electromechanical multiplier



Dec. 14, 1954 w GRAY 2,696,946

ELECTROMECHANICAL MULTIPLIER Filed D80. 1, 1948 2 Sheets-Sheet l 3'mnenlor 49 5 gay/v W axe/1y Gttorneg Dec. 14, 1954 J. w. GRAY 2,696,946

ELECTROMECE-IANICAL MULTIPLIER Filed Dec. 1, 1948 2 Sheets-Sheet 2 JOHN w G/EAY 2 .07%

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(Ittorneg United States Patent 2,696,946 ELEcrnonmcnANIcAn MULTIPLIER John w.- ray, White PlainstN; Y}, ass'i gnor' to Genet-n Precision Laboratory Incorporated,- a corporation of New York- Application' December 1, 1948;. Serial? No. 62,947 13 Claims.- e1.- 235-61 This inventionrelates to, a computer of theclass of continuously actingcomputing instruments known as function generators. v

A purpose of this invention is theprov-isionof-a mechanisrn and method for resolving a vector quantity into its two-dimensional coordinates by the trigonomet'ric solution of a right triangle. 7 This involves, in the solution for eachof the two coordinates, the finding. of the sine or cosine of agiven; angle andthemultiplication of that sine or cosine by a givenfactor.

Another purpose of this invention is the provision of Incchanismsand methods for the electrical. conversion of an input angle into the sine or cosine of that angle and the multiplication. of the result by a second input datum in the form of an electrical magnitude; the resultor out.- putof the device being furnishedin a form which: can be conveniently integrated. I g g 7 Still another purpose of this invention is the provision of mechanisms and methods for finding any desired function: of anangle and multiplying the function by one or two factors.- g

These purposes are accomplishedby the provision of a function generator for generating the functions functions p I Y=WX sin Z Y=WX cos Z where W, X, and Z are input quantities and each is independently variable.

This? invention utilizes as: input data the frequency of an electrical alternating current, the voltage magnitude of the same alternatingv current, and a mechanical angle, and. produces as. outputanother electrical magnitude. When two= outputs representing. both mutually perpendicular coordinate magnitudes are desired, two such devices arerequired. One: utility of this invention lies in its provision of a: simple; automatic, and continuous. so.- lution of the above=described avi'gational-z problem when the inputs are a frequency and an angle, or a voltage, a frequency, and an angle, with the presentation of the output data in: easily usable: electrical form, readily integrated if required. The solution is=. obtained without use of rlnovi'ng parts except for the shaft for setting the input ang e:

The: output of this invention, which may be: an elec trical' voltagev or current, can be employed to energize an integrator which may be of any one; of a number of types, so that if, the problem to be solved: is: that of the resolution ofthe movement of a vehicle over the eartlis surface intonc'arthv and east components, the total distance traveled in. latitude of irn longitude will be given by the outputof the integrator, either in miles, in degrees of latitude or longitude, Orin-present position in degrees, while the instantaneous rate of travel in latitude or longitude constitutes the input to the integrator. Such an integrator is described: in acopending application, Serial No. 5-1,6l0;filed September 2-8,. 1948 of John" W. Gray, now

- Patent No. 2,622,231.

Such a function generator can be used for the solution of problems involving two independent variables such as the solution of a right triangle when the hypotenuse and one acute angle are given. It inay thus be of use in numerous fields, forexample, in navigation, and. in fire con- 1 trol equipment. It is of particular use in the resolution of a straight line having magnitude and direction into two mutually perpendicular coordinates in its plane, and may be applied, for instance, to the resolution of the speed of a vehicle in any direction on the earths surface into its'fcoordinate speeds in the north-south and east-west directions. I

Such a function generator can also be used for thsolution' of problems involving three independent variables as, for instance, in the resolution of the speed of an aeroplane into its north-south or east-west component with correction for the geoidal shape of the earth. This is of particular importance in polar avigation. In the solution of such a problem the speed on course of the aeroplane would be multiplied by the sine or cosine of the course azimuth angle and by a function of the latitude. The product, integrated, would represent the present latitude or longitude of the aeroplane corrected for the departure of the earths shape from spherieity. v

Theffu'nc'tio'n enerator consists principally an electtost'atic variable coadensr and a converter for irre relectrical current. the magnitude of to the settin of condenser and to the frequency and voltage magnitude of alternating current supplied to the condenser.

There are a number of computing mechanisms for finding the sine or cosine of an angle,- and' for multiplying twoquantities, such as the. sine-cosine potentiometer, two-phase electromagnetic solver, ball-disc variable speed drive, pin ca-rhs and differentials, and various arrangements of two-dimensional and three dimensional cams with Scotch yokes or other follower arrangements. Some of these mechanisms involve: the movement of mechanical linkages, others are cumbersome and expensive, or are not easily adaptable to the input and output data here employed.

The instant inventionrequires very few and simple components which may be easily designed to give results of very high precision, and which have a minimum of moving parts. These components include primarily only a condenser for developing the sine, cosine, or other funcrich and a converter composed of four thermionic diodes.

I The eiia't nature of the invention will be more readily apparent from the detailed description when taken together with the accompanying drawings, in which:

Figure lis a schematic diagramof one embodiment of the computer.

Figure 2 is a front view of a sine condenser adapted for use in the computer of the instant invention.

Figure 3 is a side view of the sine condenser of Fig. 2.

Figure 4 illustrates the method of design of a sine condenser.

Figure 5 is a schematic diagram of another embodiment of the computer. 7

Figure 6 shows schematically one arrangement of a load, energized from one point of the rectifier bridge.

Figure 7 shows schematically another arrangement of a load, energized from two points of the rectifier bridge.

One embodiment is shown in Figure 1, in which a differential, variable, air dielectric, electrostatic, sine condenser 11 consists of a movable set of rotor plates 12, one fixed set of stator plates 13 and a second fixed set of stator plates 14. An alternating voltage input, indicated diagrammatically by the generator 42, is fed to rotor 12 and theoutput derived from the two sets of stator plates is fed to a diode bridge 16. This condenser is termed differential because it is' actually two condensers, the capacitance of one decreasing when the other increases and the difference between these two capacitances at any time, or the differential capacitance, is effectively utilized. The output of the computer is proportional to this differential. One capacitance exists between. rotor 12 and stator 13, while the second capacitance eit'ists between the same rotor 12 and stator 14.

The mechanical construction of this" condenser is such that ns differe m1 capacitance is proportional to the sine of its an ular setting, that is Y C1Cz-sine (1) where C1 is the capacity between rotor 12 and stator 13, C2 is the capacity between rotor 12 and stator 14, and 9 is the angle of adjustment of the condenser rotor shaft. This is further illustrated in Figs. 2 and 3 showing a front and side view of such a sine condenser. The set of rotor plates is represented by a single plate, 17, of approximately elliptical shape, fastened to shaft 18 by which the rotor can be rotated. The shaft 18 bears a pointer 19 lying in the direction of the shortest dimension of the rotor, for reading on a dial 21 the angle of setting of the rotor. When the condenser is applied to computation of the sine of an angle the zero of the scale is positioned as shown between the two stator sets of plates while for computation of the cosine of an angle the zero is displaced 90 from this point, and such a condenser, otherwise identical with a sine condenser, is here termed a cosine condenser. It is to be understood that descriptions herein of sine condensers apply equally to the cosine type except for this difference in zero of the angular data input.

The shaft is borne by two insulating blocks, 22 and 23, which support it mechanically on the stator plates while insulating it electrically from them. The two sets of stator plates, 13 and 14 in Fig. 1, are indicated in Figs. 2 and 3 by two semi-circular plates 24 constituting the first set, and two semi-circular plates 26 constituting the second set. ably made larger than the rotor to minimize edge effects. All of the first set of stator plates are connected to conductor 27, all of the second set to lead 28 and the rotor to conductor 29.

The shape of the rotor plate may be calculated from the relation expressed supra in Relation 1 if fringe effects be neglected. In Fig. 4, 31 and 32 represent two stator plates which are very close to each other at line 33. Rotor plate 34 is pivoted at 36 and is shown oriented with the direction of its shortest dimension 37 at an angle to the junction line 33 so that greater capacity exists between the rotor and plate 31 than between the rotor and plate 32 in accordance with the well-known relation where C is the electrostatic capacity, K is the dielectric constant, d is the thickness of dielectric and A is the effective area of dielectric. A is taken as the area of that part of the rotor which in Fig. 4 overlies a stator plate. For calculation of the capacity between the rotor and stator plate 31 this area is that enclosed above line 33 indicated as A1, and for calculation of capacity between the These stator plates are preferrotor and stator 32 the area is that below line 33 indicated as A2. Relation 1 then may be written A1-A2=k sin 0 where k represents at K and a dimensional constant. Differentiating Equation 3 the expression 1 dA1dA2=k cos (M0 is obtained.

In I ig. 4, a clockwise rotation of the rotor until the line 41 coincides with line 33, being a displacement through angle 11!), increases the area A2 covering stator 32 by /2r1 d0, where r1 is the radius from center 36 to point 39, minus /irz do, where r2 is the radius from center 36 to point 38. Similarly, area A would be decreased by the same amount, so that Equation 4 becomes condenser used in this invention need not be confined to such a shape as to resolve the condenser displacement angle in terms of sine or cosine. The displacement angle may instead be resolved in terms of any other function required by the intended use by the same general design procedures outlined supra, within limitations of mechanical design. For instance, if a function such as tangent is to be employed the useful movement must be restricted to less than 90 in each quadrant since at values of this function near infinity the physical sizes and relationships of the condenser parts would become impracticably large.

Returning to Fig. 1, the alternating current generator 42 supplies alternating charging voltage to the differential condenser 11. This generator preferably should supply a square or other flat-topped and flat-bottomed waveform voltage, but may supply an alternating voltage of any form so long as the shape is fixed and the peak-to-peak voltage is definite and under control. The frequency of the voltage output of this generator comprises one input datum; its voltage magnitude may be employed as a second input datum.

Generator 42 charges rotor 12 alternately positively and negatively with a quantity of charge Q=CV, where C is the total capacity of rotor 12 and both stators 13 and 14, and V is the potential to which charged. The same charge is applied by induction to each of the stator plates 13 and 14 in the proportion of their respective capacities C1 and C2, each receiving substantially its entire charge, positive or negative, during any positive or negative half cycle because the capacities and resistances are made such that the time constants are small compared with the duration of a half cycle. The total quantity of positive or negative charge applied through a stator set 13 or 14 to the diode bridge 16 in one second will therefore be the quantity per half cycle multiplied by the number of cycles per second, or the frequency 1 of the output of generator 42. Positive charges on the stator 13 will flow through diode 43 to ground when the voltage is above that of fixed bias battery 52 and negative charges on stator 14 will also fiow to ground through diode 44 when more negative than the potential of battery 53. On the other hand negative charges on plates 13 will flow through diode 46 into condenser 48, the other plate of which is grounded and positive charges on plates 14 will flow through diode 47, into the same condenser 48. The provision offixed bias batteries 52 and 53 acts to compel operation of the diodes over a preferred part of their characteristic.

The amount of the charge flowing into condenser 48 per second from stator 13 will be Q1=C1Vf (6) and from stator 14,

Q2=C2Vf (7) The difference will be, from Equation 1.

Q1Q2=Vf(C1-C2)-Vf sin!) (8) That is, the preponderance of negative charge (from plates 13) at point 49 of bridge 16 over positive charge (from plates 14) per second is directly proportional to the sine of the angle at which the shaft of condenser 11 is set multiplied by the voltage and frequency. Now if the potential of point 49 be kept at some fixed reference potential, the preponderance of positive or negative charge at this point will flow off as fast as impressed thereon and the rate of flow, or electrical direct current, will be a direct measure of the above angular setting. That is,

i1=kQ1 where i is the current flowing through diode 46 from Now, choosing any convenient ratio between r1 and r2 for condenser 48 due to charge Q1 from plates 13, and k is a proportionality constant. Similarly i2 being the current flowing through the diode 47 toward the condenser 48 due to the charge Q2 from the plate 14. Theseequations are simply the statement of the basic definition ,of current as the amount of charge which flows in unit.tirne.

Since it has been assumed that" the point 49 is kept at a fixed potential, the current is supplied through conduct or 50 Inust -eqnal the dilference :of the currents .i; and 112,0; from ($1,199 and( I) Lead "50, s semester! t a lead wh sk m y eat any type that can supply a current suchas i3 and indian: it ma n tude w i e P eferabl no requir ng an power to b sup l ed t t t ro ead 5 a d Pre e abty e159 tarn shi an ind at on of the time nte ral of t e cu n 1 Senegal forms of such load can he constructed, and for purposes .of illustration the form may consist of a Y n/hi h a a m e a mo ore erat a ashametr and a counter as illustrated .in Fig, 6. Here the input ier als 49 a d 1 are e same s h lik -1 4mhare t ann s Qt E steams 4. i ma' a ts'd. hasta y at around P n i l, by ne at 'is si apls a ri isa "mm-u h he qfn is ji g ma 1 8 e e ator fiii andfresistor"4, T x H itude of-currentsupr l h ou h this loop. s' ptqvrwnnal 9 the rsed 1 f se e aqr ...'h. h i nd a ed by tachome er scan- 1 whiah 1h e ore al ndica t prqduct o inp vqltage. inpu f quency, and t sins, o qn e' ss an e- Th {me integr l of t is Pr du i in icatl cl yY h'e accumula e reading f n Wishi g YQ l' iQ -S Qt sh 'fi'r6 hap e in t e moto to the sener t r When the instant invention isranpl ed to c str nn of. a, res lver such as"u ightbele pl yed in s l na lica n w t t-e uate fp apo ional to s e d Q 'tl 1e nd masisa's a s e ar pmenac e Qt h co rse uth'angl'e, the current is will he represe atiye of the c ,pone of speed n anew-W s dire. if the 'de er is a sine resolver, and will be representative oi t component .of speed in a norihiwuth d sc on if he. 9 u er i a c s ne r snlve e inte ral o h'! cur nt is in ea a e Will of amuse be thet l d tans r v n e snvest and is th puth 41., a

ti nsresn siyelw 'nse t e ut u ect ic uant y i his n ention is ually p opo a t9 e wh n? as w ll as, the

frequency-o th inpu en r qr, v l age instead of the f equency m ht e ilized in the above examp e as one of the data. Whichever i not so used, Yelp as; or ie/91 s.. m be he d c ns ant, or t maybe m demanua l adj s b e in rQ -ids a aravan-lent v rat n l sa i t nn adjustment, r t ay bsused as. a ea l cqr. cti ata input s p e i m ntionedis tn Fi 1, l d 51 ma e con uc d a t an as the terminals Of-F-ig. 1 bearing identical refarenas c a acte L i e assume a ring opera tion t pa ential au s hese t minal vari s sl ghtly so that th P en ial o inal 4 i 6, end tcr'is l lyhen hi re uct o o bia 'ot th grid 4 wit 're p c' b its catho e 152 l re ult in an a a anode current 'flow through the tube 149," Sn -an iuqrsas d cu -ren fl w owever e ul n a de r as pot ntial e n ap ied to the has l 157 a a r .t o fliei a e m n h a od re s ar'fifi," hi

.65 n 6111,0333.PQWWRYHKQMS? res l in a r the'p sa ia ap lied. a t e a 1 1 Seth h hi d as spect t when 5 1 a, lug in a reduced anode current flow in thi s 'tube. i d rren of t lh wsv n fl w hro ish the r'sistpr c n e e n h 'sathpde c r uit Q'f tu e 4 Sb that af ed t in t 'ur s redu e th anemia dropproduced'a'cross this resistorand hence reduces the potential .Of the cathode 152. Because it is the "rennin po'tential of cathode and grid whichf'cont'rolsthe"qilip'ut 1 e tube; he ene b'de Ti s ia amsu'n' s' to the same thing as an increase in potential of the grid and it is not necessary for the grid potential to increase t i a e the tp t o the tube: a m

' first glance, may sent paradoxical that an increase ininput applied to'the terminals}? and 61' may result in an incrasein 'out'put'withoi t' a concomitant increase of potential 'at'the grid 148 'but circuitparauieters may be so chosen forthe interconnected networkaboved'escribed that not only may thepotential'of the cathode 152 be so varied in an opposite direction as to -cau'sefthe grid potential to remain stationary "evea reasonable operating range but even over-compensation main; obtained if such were desired whe by the? "d lama! is actually deci eased as the in 7 situation obtains, of course, onlyiip to theses-am Fig- Whe e inp t'ls' minals 42 @5 51 a r s ftionoi ,onithe input of tube .166 through the network consisting of resistors lo'lrand lfir9 iandcondenser 168. The output of tube 166 is in'turn resistance coupled to the input of the final stage 171 which has .itsvca-thode 172 connected to have a small alternating current potential impressed thereon from the alternating current-source 1-73'so that the bias on this tube fluctuates ibetween limits which are determined byxthe signal potential applied to the grid 17%.

There will "be then an fluctuating current in :the anode circuit of this tube the av'era-ge valuesof which is determined by the signal potential applied to ahe inputof the tube. This-fluctuating potential is caused to flo'w vthrough th'eactuatingcoil 1760f 'a relay 177which additionally includes a pair -of substantially iixed contacts 178 and 1 7:9 vand a spring-armature 1&1 actuated by the current flowingin th'ecoil'1 76. The circuit parameters are such and the armature 181 is so biased by spring vA59 that when t here'is a certain input to the :tube 171, the fluctuations of anode current thereof are such :as to cause the armature 181 to engage the contacts 1T8 and 179 for equal lengths of time 'as the anode current fluctuates from its makimurn' to its minimum as a result of the alternating potential impressed on the cathode 172. When, however, the signal potential is increased the vaverage anode current is also increased and the armature l8l' will be caused to engage thecontact 178, 'forexarnple, for 'a larger period of time during acyclic variation than it engages contact 179 and conversely. :When the signal potential'is decreased the armature-181 "engages the-'contact'1'79 for a longer period of time than :it engages "the contact 178, the relative periods :of time lbe'ing dependent on the value of the signal potential. Y

Thisaction controls the-direction and speed of rotation of the motor 182 in the following m nner: The motor 182 is a '-two .phase lrno'tor having field coils"183 and 18,4- wound out ofphase as respects each other. If these field :coils are supplied with alternating current energy and :the'current in one coil is made :to lead the other by 9.0:" the motor will rotate in one direction whereas if the currents in the second coil is made to 'lead that in the first byr90- "the motor will rotate in the opposite direction. -When the armature 181 engages contact 179, alternating current is supplied from the source 186 to the field coil183 through a circuit which includes the conductor 87, armature I81, contact 179, conductor 188, field coil 133 and conductor 190 "hack to thesource-lil. On the other hand, the circuit 'which supplies energy to the field coi-l'1f84 includes the conductor 8-7, armature 181, contact "179, eOnduetoF-ISS,"condenser -187,"fie1d coil 184 and conductor 190. Because the condenser 187 is included in' the circuit which energizes the field coil 184 the current through this'coil leads thatsupplied to coil 183 by 90 and the torque applied to themotor is such as to'cause it to tend to rotate in say a counter-clockwise direction. When, however, the armature 181 is caused to engage the contact 178 i't'wi lI be apparent that'the circuit connections are reversed, the eondenser 187 now being included in the'circuit which energizes field coil 183;aridfi'e1d coil 184' being csnriec ed' directlylo the source. This current'f lowing through the field coil 183, h f e 9? le t fishin t rsuah fie d i lsa andth'e torque applied 'to the m s; is such as to cause it"t'otehd tdrotafein' a clockwise direction, I the a ma r W s b te pi sa at i y sys s Psi a i il this rm u e-en a e nta s 178 and. 179 for enactlyegual ihtervals of time, the rnotor 182 'Wil en to to first in 9 s d re tion an hen he o he nder equal and ppq'site torqu mpulses. Be.- ca'usefthe motor some inertia and the equal and npnow'te ton ng: impu a ap y pp ied no. rotation will occur. the a turelsl engages one 17. d 79 r nter-val thanit rewill bs tam tonne de el ed 182 which will tend to rotate it in one direction or the other at a speed which is determined by the relative time engagement of the contacts 178 and 179 and hence the relative unbalance of opposing torques developed in the motor.

It will be apparent, therefore, that the varying signal input to the tube 171 will produce a rotation of the motor 182 in one direction or the other at a speed which is approximately proportional to that input' The motor 182 rotates shaft 68 which is connected to tachometer 66, counter 67 and generator 63. The latter supplies current to point 49 through resistor 64 of resistance R1 so that current is will be supplied to terminal 49 of such polarity as to neutralize the slight tendency of that terminal to change in potential.

A memory circuit consisting of resistor 194 and capacitor 193 eliminates the effect of short-time disturbances and prevents any tendency to hunt as is fully described in the copending application, Serial No. 51,610, filed September 28, 1948, of John W. Gray.

A second embodiment of this invention is shown in Fig. employing alternating voltage take-off to the utilizing load instead of direct current take-off. The generator 42. differential condenser 11. and diode bridge 16 all are of the same structure and operation as described in connection with Fig. 1. Likewise, the outputs of the stator plate sets 13 and 14 consist of quantities of electricity proportional to the product of the voltage and frequency of the square wave input and of the designed function of the input condenser angle, and resulting in currents i1 and i2 flowing into and out of terminal 49, w h his e a n r n v i ained at a constant reference voltage by the introduction of difference current i3 from some source in the utilizing load. However, the signal to the load is not taken from terminal 49. but to secure greater stability is taken from terminals 54 and 56, which are those terminals of the diode bridge to which the sine condenser 11 is connected. These terminals will normally fluctuate in square wave manner over a small voltage range, and when the bridge is in balance these volta es will be equal. These voltages are impressed on an alternating current differential amplifier 57, the output of which is connected to and operates a l ad 58 which may be any desired ty e of integrator. The am lifier also normallv supplies the current is demanded by terminal 49 at balance.

This o eration is accomplished as follows: Assume that fixed bias batteries 52 and 53 have potentials of e1 and e v lts. and that i1-i2=is. Then when the stator 13 is ositive, it must be more positive than the potential e before current will flow through tube 43 to ground, and when this stator is negative it must be more negative than ground potential before current will flow through tube 46 from terminal 49 and condenser 48, causing the terminal 54 to fluctuate between ground potential and er volts. Similarly terminal 56 will fluctuate between ground p tential and 22 volts. These two potential ranges will therefore equal e1 and 2 respectively and by making 2 equal to era. the differential input to amplifier 57 will be zero. If, however. any input data chan e varies currents i or i2, their difference no longer will eoual the current i3, and because of the drop in resistor 59 the potential of point 49 will depart from its reference value. increasing one output voltage and correspondingly decreasing the other at the terminals 54 and 56 connected to the input of the amplifier 57. Thus a differential voltage will ap ear at the amplifier input with the result that the amplifier output will be varied and more or less current, is, will be produced as the situation may require, restoring the balance and reducing its differential input voltage to approximately zero. The variation of amplifier output which as indicated by Equation 11 is a function of the input voltage, its frequency and the position of the rotor shaft may then be utilized to operate a l ad 58 in any desired manner depending on the application to which the invention is put.

One form of amplifier 57 and load 58 which has been successfully operated is shown in Fig. 7. Here input terminals 54 and 56 and current output terminals 49 and 61 correspond to the terminals in Fig. 5 bearing the same reference characters. The fundamental difference bet een th s f rm of d and that of g. 6 is that here the input signal is applied at a point different from that from which the compensating current is is taken.

When the capacities of condenserstators 13 and 14, Fig. 5 are equal,' currents i and iz are equal and potential changes effective on terminals 54 and 56, Fig. 7 will be equal. When these potentials are impressed on grids 71 and 72 of triode tubes 73 and 74 through blocking condensers 76 and 77, their zero reference voltages are shifted so that simultaneously equal potentials appear on these grids. Opposite phase potentials are applied from the plates 101 and 102 to the grids 103 and 104 of triodes 106 and 107, which constitute a phasedetecting amplifier. This amplifier produces a direct current differential output, operating on only alternate half cycles of input as follows: Its cathodes 108 and 109 are energized at input data frequency from generator 42, which is the same generator depicted in Fig. 5, through resistor 111. During positive half cycles no current will flow through tubes 106 and 107 because their cathodes are highly positive with respect to their grids, but during negative half cycles current will flow. During such half cycles the currents are under control of the grids, so that if a grid is more positive, more current will fiow and the plate potential will drop due to loss in the plate resistor. Since the two grids are in phase and equal at all instants in potential, the two plate potentials will be equal. Condensers 114 and 116 are made large enough to substantially smooth the output over the cycle, so that direct voltage is applied to grids 117 and 118 of the direct current amplifier 79. The outputs of direct current are impressed on saturable transformer 81. This transformer has saturating windings 82 and 86 and primary windings 83 and 88, associated respectively with secondary windings 84 and 89. Primaries 83 and 88 are energized by a 400-cycle source at terminals 91 so that the secondaries 84 and 89 may be energized in opposite phase. Therefore in absence of current in the saturating windings 82 and 86, maximum output voltages are generated in secondaries 84 and 89 but they exactly cancel each other, being of opposed phase. and no current flows. When. however. current flows only in winding 82, the associated core is at least partly saturated, and less voltage is induced in secondary 84, so that some current is produced by the voltage in secondary 89. Conversely, current in winding 86 alone reduces the induced voltage in secondary 89. inducing an output current of the phase of secondary 84. With equal saturating currents there is no output current. The two secondary windings are connected in series to a winding 92 of a two-phase motor 93, the remaining winding 94 of which is connected at terminals 96 to a 400-cycle source whose phase is in quadratu e to that which mav energize winding 92. The latter will have a phase which momentarily de ends on whether the current received from secondary 84 is greater or less than the current, out of phase. received from secondary 89. It follows that motor 93 will run in one direction when under control of secondary 84. and in the op osite direction when under control of secondary 89, and if equal currents are received from these secondaries the motor will remain stationary. This is the condition in the assumed case.

If currents i1 and i2 become unequal, voltages applied to grids 71 and 72 no longer remain eoual, so that the amount of saturation due to primary 82 no lon er remains equal to the amount of saturation due to rimary 86. and current from one secondary preponderates over that from the other. causing motor 93 to rotate. This operates tachometer 97. indicating the speed of rotation proportional to frequency. pote tial and condenser an le at the com uter. and counter 98, indicating the inte ral of the product of these f ctors. and generator 99. which produces a current i3 and sunnlies it t termin l 9 to balance the computer. Since this amplifier and feedback may be m de verv hi h in gain. a small change in compger conditions can be made to produce a large indicated e ect.

Wh t is claimed is:

1. In a com tin instrument of the f ncti enerating type. a differential c ndenser having the difference of its capacit nces c m rising a first quantity, an altern tin ge er tor Whose output comprises a second quantity. circuit mea s connecting one terminal of said e erator to s id differenti l condenser, a four-arm bridge comprising four rectifier elements, an electrosta ic fixed condenser connected between one pair of bridge terminals, circuit means for connecting a first termi l of s id fixed condenser to ground and to the remaining terminal of said generator, means for maintaining thesecond terminal of said. fixed condenser substantially at ground potential, circuit means for con meeting said differential condenser output to the two remaining bridgeterminalgantl means forabstracting from said bridge an electrical quan ty representative of the productof said first and second quantities.

' '2 A" device according toclaim 1; in which said circuit means for abstracting from-said bridge an electrical quantity" representative of the product of said first: and second quantities is electrically connected to said second terminal of the fixed condenser.

3. A device according to claim 1 in which said circuit means for abstracting from said bridge an electrical quantity representative of the product of said first and second quantities is electrically connected to said two remaining bridge terminals.

4. In a computing instrument of the function generating type for generating the product of a first and second quantity and of a third quantity representing a function of a shaft displacement angle, an electrostatic variable rotary difierential condenser comprising two capacitors which vary in opposite sense as functions of the angular displacement of a common actuating shaft, the difference of the capacitances of said two capacitors being proportional to a specific function of said angular displacement and comprising said third quantity, an alternating generator whose frequency of alternation comprises said first quantity and whose output potential cornprises said second quantity, circuit means connecting a terminal of said generator output to said difierential condenser input, a four-arm bridge comprising four rectifier elements, a fixed condenser connected between one pair of bridge terminals, circuit means connecting one of said pair of terminals to the remaining terminal of said generator and means for maintaining the remaining terminal of said pair of terminals substanitally at the potential of said last-mentioned generator terminal, circuit means for connecting said differential condenser to the two remaining bridge terminals, and means for abstracting from said bridge an electrical quantity representative of the product of said first, second and third quantitles.

5. A device according to claim 4 in which said differential condenser rotor has flat plates approaching an elliptical shape rotating eccentrically about a point in the minor axis, and substantially satisfying the geometrical re ation where. r1 and r2 are two opposite radii and 0 is the angle made by one radius with the minor axis.

6. In a computing instrument of the function-generating type for generating the product of a first and second quantity and of a third quantity representing a function of a shaft displacement angle, an electrostatic variable rotary differential flat-plate condenser comprising two capacitors which vary, in opposite sense as functions of the angular displacement of a common actuating shaft, the rotor of said condenser approaching a substantially elliptical shape satisfying the relation where r1 and r: are two opposite radii and 0 is the angle made by them with the minor axis, whereby the difference of the capacitances of said two capacitors is proportional to the sine of 0 and comprises said third quantity, an alternating generator whose frequency of alternation comprises said first quantity and whose output potential comprises said second quantity, circuit means connecting one terminal of said generator to said differential condenser input, a four-arm bridge comprising four thermoelectric diodes disposed singly each in one of the four arms of said bridge, circuit means connecting the plate of each diode to the cathode of an adjacent diode, a fixed condenser connected between one pair of bridge terminals, circuit means connecting one of said pair of'terminals to the remaining terminal of said generator and means for maintaining the remaining terminal of said pair of terminals substantially at the potential of said last-mentioned generator terminal, circuit means for connecting said differential condenser to the two remaining bridge terminals, and means for abstracting from said bridge at last-mentioned terminal of said fixed candenser an. lectrical quantity tq rescntativ c the pro saidflrst; se ond and. hirdq en i ie z 7'. In a computing'instrunrent; of the function-generatingtyperfo'r generatingthe product of" a first and second quantity and" of a third quantity representing a function of a shaft displacement angle, an electrostatic variable rotary diife 'rejntial fiat-plate condenser comprising two capacitors which Va l)? in oppositesense as functions of the angular displacement of a common actuating shaft, the rotor of saidj condenser' approaching, an" ellipticalsh'ap'e substantially satisfying the relation where n and n: are two opposite radii and 0 is the angle made by them with the minor axis, whereby the difference of the capacitances of said two capacitors is proportional to the sine of 0 and comprises said third quantity, an alternating generator whose frequency of alternation comprises said first quantity and whose output potential comprises said second quantity, circuit means connecting one terminal of said generator to said difierential condenser input, a four-arm bridge comprising four thermoelectric diodes disposed singly each in one of the four arms of said bridge, circuit means connecting the plate of each diode to the cathode of an adjacent diode, a fixed condenser connected between one pair of bridge terminals, circuit means connecting one of said pair of terminals to the remaining terminal of said generator and means for maintaining the remaining terminal of said pair of terminals substantially at the potential of said last-mentioned generator terminal, circuit means for connecting said differential condenser to the two remaining bridge terminals, and means for abstracting from said bridge at said two remaining bridge terminals an electrical quantity representative of the product of said first, second and third quantities.

8. A device according'to claim 7 in which said first quantity comprised of the frequency of alternation of said generator, said second quantity comprised of the output potential of said generator, and said shaft displacement angle are three independently variable quantities constituting the computer input data.

9. A device according to claim 7 in which said first quantity comprisedof the frequency of alternation of said generator, and said shaft displacement angle are two independently variable quantities constituting the computer input data, and said second quantity comprised of the output potential of said generator is a constant.

10. A device according to claim 7 in which said second quantity comprised of the output potential of said generator, and said shaft displacement angle are two independently variable quantities constituting the computer input data, and said first quantity comprised of the frequency of alternation of said generator is a constant.

11. In a computing instrument of the function-generating type for generating the product of a first quantity and of a second quantity representing a function of a shaft displacement angle, an electrostatic variable rotary differential flat-plate condenser comprising two capacitors which vary, one directly and one inversely, as functions of the angular displacement of a common actuating shaft, the rotor of said condenser approaching an elliptical shape substantially satisfying the relation where n and rz are two opposite radii and 0 is the angle made by them with the minor axis, whereby the difference of the capacitances of said two capacitors is proportional to the sine of said angular displacement and comprises said second quantity, an alternating generator which generates an electrical quantity comprising said first quantity, circuit means connecting one terminal of said generator to said differential condenser input, a fourarm bridge comprising four thermoelectric diodes disposed singly each in one of the four arms of said bridge, circuit means connecting the plate of each diode to the cathode of an adjacent diode, a fixed condenser connected between one pair of bridge terminals, circuit means connecting one of said pair of terminals to the remaining terminal of said generator and means for maintaining the remaining terminal of said pair of terminals substantially at the potentialof said last-mentioned generafor germinal, circuit means for connecting said difitlerentiadl References Cited in the file of this patent con enser to the two remaining bridge termina s, an means: for abstracting from said bridge an electrical UNITED STATES PATENTS quantity representative of the product of said first and Number Name Date second quantities. 5 1,620,020 Hardy Mar. 8, 1927 12. A computing instrument in accordance with claim 2,401,527 Vance June 4, 1946 1 1 in which said electrical quantity comprising the first 2,433,236 Rajchman et a1. Dec. 23, 1947 quantity is frequency of alternation. 2,433,237 Rajchman et al. Dec. 23, 1947 13. Acomputing instrument in accordance with claim 1'1 in which said electrical quantity comprising the first 10 quantity is generated potential. 

